Learning the concept of integral through the appropriation of the competence in Riemann sums

Abstract

It is proposed that the difficulty of engineering students into understanding the concept of the integral, as a way for calculating the area under a curve, can be overcame if students are taught how to translate it into the problem of calculating a Riemann sum. A series of applied problems are proposed to provide a frame that required to calculate the area under a curve to two groups of students. For one of these groups, Geogebra was proposed as a tool that could be used to maintain the focus of students into the concepts, by providing ways to easily calculate and visualize the solutions, while the other group reached to the solutions by analytically making all the calculations. Evidence was found that, to a confidence level of 95%, Riemann sums calculated with Geogebra reduce the score difference in context problems requiring the calculation of integrals, helping students to reach a better understanding on the concept of the integral as the area under the curve of a given function.